A combinatorial approach to products of Pisot substitutions




Berthe V, Bourdon J, Jolivet T, Siegel A

PublisherCAMBRIDGE UNIV PRESS

bri

2016

Ergodic Theory and Dynamical Systems

ERGODIC THEORY AND DYNAMICAL SYSTEMS

ERGOD THEOR DYN SYST

36

1757

1794

38

0143-3857

DOIhttps://doi.org/10.1017/etds.2014.141(external)



We define a generic algorithmic framework to prove a pure discrete spectrum for the substitutive symbolic dynamical systems associated with some infinite families of Pisot substitutions. We focus on the families obtained as finite products of the three-letter substitutions associated with the multidimensional continued fraction algorithms of Brun and Jacobi-Perron. Our tools consist in a reformulation of some combinatorial criteria (coincidence conditions), in terms of properties of discrete plane generation using multidimensional (dual) substitutions. We also deduce some topological and dynamical properties of the Rauzy fractals, of the underlying symbolic dynamical systems, as well as some number-theoretical properties of the associated Pisot numbers.



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